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Quadratic discrete Fourier transform and mutually unbiased bases
Kibler M. R.
Dans Fourier Transforms: Approach to Scientific Principles, G. Nikolic (Ed.) (2010) 103-138 - http://hal.in2p3.fr/in2p3-00530340
Physique/Physique Quantique
Physique/Physique mathématique
Mathématiques/Physique mathématique
Quadratic discrete Fourier transform and mutually unbiased bases
Maurice Robert Kibler ()1
1 :  IPNL - Institut de Physique Nucléaire de Lyon
http://www.ipnl.in2p3.fr/
CNRS : UMR5822 – IN2P3 – Université Claude Bernard - Lyon I (UCBL)
France
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier transform. This Fourier transform can be considered as a two-parameter extension, with a quadratic term, of the usual discrete Fourier transform. In the case where the two parameters are taken to be equal to zero, the quadratic discrete Fourier transform is nothing but the usual discrete Fourier transform. The quantum quadratic discrete Fourier transform plays an important role in the field of quantum information. In particular, such a transformation in prime dimension can be used for obtaining a complete set of mutually unbiased bases.

Chapitres d'ouvrages scientifiques
2010
Fourier Transforms: Approach to Scientific Principles
G. Nikolic
103-138
InTech (Open access Publisher) Vienna

03.65.Fd, 03.65.Ta, 03.67.-a, 02.20.Qs
36 pages, submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011 - ISBN 978-953-307-231-9
quadratic discrete Fourier transform – mutually unbiased bases – Weyl pairs – Pauli operators – Lie algebras
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